Venezuelan voters began casting their votes at 06:30 a.m. local time (1100 GMT) on Sunday. The polls will close after 10 hours unless there is need for extending voting hours due to high turnout.
It will be the second time in just over six months that voters in the South American country have cast ballots in a presidential election.
Chavez, who ruled Venezuela for 14 years, celebrated a triumphant re-election victory in October 2012. After his death on March 5, authorities announced new elections to select his successor.
The two main candidates are acting President Nicolas Maduro and opposition leader Henrique Capriles. Opinion polls have given Maduro leads ranging between 10 and 20 points. However, the last survey carried out by the Caracas-based Datanalisis polling firm gave him a narrower 9.7-point edge last week.
Maduro, 50 and a candidate for the United Socialist Party of Venezuela, has promised to continue the late Venezuelan leader’s policies which helped to slash poverty from 50 to 29 percent.
Capriles, a 40-year-old state governor and the representative of a coalition of opposition parties, blames the government for the nation's economic woes. He lost the presidential election to Chavez by a nearly 11-point margin in October 2012.
Maduro on Saturday called on the Venezuelan nation to participate in the election, saying, “We believe we will break the record of turnout.”
He said he would respect the vote result and urged the opposition to avoid falling for the provocations of foreign countries trying to create unrest in the country.
Several plots have been foiled so far to destabilize the elections. In the latest incident on Friday, Venezuelan vice president Jorge Arreaza announced that security forces had arrested two Colombian paramilitaries who planned to sabotage the election.
More than 18.9 million Venezuelans are registered to vote in the presidential election. Venezuela's National Electoral Council estimates that more than 100,000 Venezuelans will vote abroad at diplomatic offices in 88 countries.
In addition to more than 3,000 representatives from national organizations serving as observers, Venezuela's National Electoral Council says 170 international observers have been invited to witness the elections.